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2 years ago

The ____ of a triangle is the center of the only circle that can be inscribed inside it

Mathematics

2 answers:

Artist 52 [7]2 years ago

8 0

Answer: INCENTER

Step-by-step explanation:

APEX

GREYUIT [131]2 years ago

4 0

The circumcenter <span>of a triangle is the center of the only circle that can be inscribed inside it.

I hoped I helped!</span>

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2 years ago

Suppose (ideally) a hammer claw moves a distance of 0.10 meters to remove a nail. If a resistance force of 1500 N is exerted by

dusya [7]

Answer:

7500 N

Step-by-step explanation:

Given that,

A hammer claw moves a distance of 0.10 meters to remove a nail.

Resistance force, F = 1500 N

The person move the handle of the hammer 0.5 m

We need to find the effort force. Let it is F'. The mechanical advantage is given by :

$m=\dfrac{effort}{resistance}=\dfrac{d_i}{d_o}$

Where $d_i\ \text{and}\ d_o$ are input and output distance respectively.

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2 years ago

Which equation could be used to calculate the sum of the geometric series?

Greeley [361]

$\dfrac{1}{3}+\dfrac{2}{9}+\dfrac{4}{27}+\dfrac{8}{81}+\dfrac{16}{243} = \\ \\\\ = \sum\limits_{k=1}^{5}\dfrac{2^{k-1}}{3^k} = \sum\limits_{k=1}^{5}\dfrac{2^{k}}{2\cdot 3^k} = \dfrac{1}{2}\cdot \sum\limits_{k=1}^{5}\dfrac{2^{k}}{3^k} = \\ \\\\ = \dfrac{1}{2}\cdot \sum\limits_{k=1}^{5}\Big(\dfrac{2}{3}\Big)^k = \dfrac{1}{2}\cdot \left[\Big(\dfrac{2}{3}\Big)^1+\Big(\dfrac{2}{3}\Big)^2+...+\Big(\dfrac{2}{3}\Big)^5\right] =$

$= \dfrac{1}{2}\cdot \dfrac{\dfrac{2}{3}\cdot\left[\Big(\dfrac{2}{3}\Big)^5-1\right]}{\dfrac{2}{3}-1} =-\Big(\dfrac{2}{3}\Big)^{5}+1 = \dfrac{-2^5+3^5}{3^5} = \boxed{\dfrac{211}{243}}$

$\text{I used the geometric series formula for sum: }S_n = \dfrac{b_1\cdot (q^n - 1)}{q-1}$

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